최단강하선과 등시곡선

Abstract

최단강하선(Brachistochrone)의 방정식을 세우고 변분학(Calculus of Bariations)에서의 Euler의 공식을 이용하여 이 경로를 구하는 미분방정식을 유도하며 그 해를 구한다. 이 해 Cycloid 임을 밝히고 이 곡선은 또한 등시곡선 (Tautochrone) 임을 보인다.

The equation fo the Brachistochrone is solved by the introduction fo the differential equation, which is obtained by using Euler's formula on the Calculus of Variations. The solution of the diffenential equation is the cycloid, which is the Tautochrone, too.

The equation fo the Brachistochrone is solved by the introduction fo the differential equation, which is obtained by using Euler's formula on the Calculus of Variations. The solution of the diffenential equation is the cycloid, which is the Tautochrone, too.